The NFL handed out modified suspensions Tuesday to four players involved in the New Orleans Saints’ alleged bounty program.

Linebacker Scott Fujita, who now plays for Cleveland, saw his suspension reduced from three games to one. The suspension of defensive lineman Anthony Hargrove, now a free agent, was reduced from eight games to seven. There is no change to the suspension of Saints defensive lineman Will Smith, who is still banned for four games. And linebacker Jonathan Vilma is still out for the season, although the league says he can keep the pay he earned for his six weeks on the physically unable to perform list.

The players’ suspensions were lifted last month by a three-member appeals panel that determined NFL Commissioner Roger Goodell was overstepping his authority if he was punishing the players for both conduct detrimental to the league and circumventing the salary cap. He has the authority to punish for the former, but not for the latter.

Goodell modified the suspensions, clarifying they were for conduct detrimental, and resubmitted them.

“The quality, specificity and scope of the evidence supporting the findings of conduct detrimental are far greater and more extensive than ordinarily available in such cases,” Goodell said in a written memo to all 32 teams.

“In my recent meetings with the players and their counsel, the players addressed the allegations and had an opportunity to tell their side of the story. In those meetings, the players confirmed many of the key facts disclosed in our investigation, most particularly that the program offered cash rewards for 'cart-offs,' that players were encouraged to 'crank up the John Deere tractor' and have their opponents carted off the field, and that rewards were offered and paid for plays that resulted in opposing players having to leave the field of play.”

The players now can appeal their new suspensions to Goodell to take the league back to court. Count on both sides being back before a judge.

[For the Record, 3:11 p.m. Oct. 9: The headline on an earlier version of this online post said the NFL had slightly modified the supensions of four players. Actually, only three players' penalties were changed; the suspension of defensive lineman Will Smith was unchanged.]